Mechanism of the 1-C4H9 + O reaction and the kinetics of the intermediate radical 1-C4H9O

Article abstract of DOI:10.1039/b100149n

The 1-C₄H₉ + O reaction has been investigated in two quasi-static reactors with different detection systems. From a time-resolved measurement of OH formation by laser induced fluorescence (T = 295 K, p = 21 mbar, bath gas: He) an inverted vibrational state distribution for OH X²∏ (v = 0, 1, 2) was observed. By using Fourier transform infrared spectroscopy, relative product yields of 0.55 ± 0.08 for 1-C₄H₈, 0.397 ± 0.05 for HCHO and 0.053 ± 0.02 for C₃H₇CHO were determined (T = 298 K, p = 2 mbar, bath gas: He). The results are explained in terms of the formation and subsequent decomposition of an intermediate chemically activated 1-C₄H₉O radical and a competing abstraction channel leading directly to OH + 1-C₄H₈. A modelling by statistical rate theory based on ab initio results for the stationary points of the potential energy surface of C₄H₉O allows the quantitative description of the product branching ratios. From this modeling, threshold energies of E₀₆ = 55 ± 6 and E₀₇ = 88 ± 6 kJ mol^-1 for the β-C-C and the β-C-H bond dissociation, respectively, in 1-C₄H₉O are obtained. For the 1,5 H atom shift, a most probable value of E₀₅ = 40 ± 5 kJ mol^-1 follows from a comparison of our quantum chemical results with data from the literature.

Full text of DOI:10.1039/b100149n

View Article Online / Journal Homepage / Table of Contents for this issue
Mechanism of the 1-C H + O reaction and the kinetics of the
4 9
intermediate 1-C H O radical
4 9
W. Hack,a K. Hoyermann,*b C. Kersten,b M. Olzmann*c and B. Viskolczd
a Max-Planck-Institut fur Stromungsforschung, Bunsenstrae 10, D-37073 Gottingen, Germany
b Institut fur Physikalische Chemie der Universitat Gottingen, T ammannstrae 6,
D-37077 Gottingen, Germany
c Institut fur Physikalische Chemie der Universitat Karlsruhe, Fritz-Haber-W eg 4,
D-76128 Karlsruhe, Germany. E-mail: matthias.olzmann=chemie.uni-karlsruhe.de
d Department of Chemistry, Gy. J. T eachersÏ T raining College, H-6701 Szeged, P.O. Box 396,
Hungary
Received 3rd January 2001, Accepted 1st March 2001
First published as an Advance Article on the web 9th April 2001
The 1-C H ] O reaction has been investigated in two quasi-static reactors with di†erent detection systems.
4
9
From a time-resolved measurement of OH formation by laser induced Ñuorescence (T \ 295 K, p \ 21 mbar,
bath gas: He) an inverted vibrational state distribution for OH X 2% (v \ 0, 1, 2) was observed. By using
Fourier transform infrared spectroscopy, relative product yields of 0.55 ^ 0.08 for 1-C H , 0.397 ^ 0.05 for
4
8
HCHO and 0.053 ^ 0.02 for C H CHO were determined (T \ 298 K, p \ 2 mbar, bath gas: He). The results
3
7
are explained in terms of the formation and subsequent decomposition of an intermediate chemically activated
1-C H O radical and a competing abstraction channel leading directly to OH ] 1-C H . A modeling by
4
9
4 8
statistical rate theory based on ab initio results for the stationary points of the potential energy surface of
C H O allows the quantitative description of the product branching ratios. From this modeling, threshold
4
9
energies of E \ 55 ^ 6 and E \ 88 ^ 6 kJ mol~1 for the b-CÈC and the b-CÈH bond dissociation,
06 07
respectively, in 1-C H O are obtained. For the 1,5 H atom shift, a most probable value of E \ 40 ^ 5 kJ
05
mol~1 follows from a comparison of our quantum chemical results with data from the literature.
4
9
reaction channels of the 1-butoxyl radical:
CH CH CH CH O~
1. Introduction
The reactions of alkoxyl radicals have been extensively
studied in recent years because of their crucial role in atmo-
spheric chemistry and in combustion systems1h15 (for a review
of earlier work, see e.g. refs. 14È16). Whereas for small alkoxyl
radicals under tropospheric conditions the bimolecular reac-
tion with O to form carbonyl compounds and HO domi-
3
2
2
2
] CH CH CH CH(~)OH
( ] É É É) (2)
( ] É É É) (3)
( ] É É É) (4)
( ] É É É) (5)
(6)
3
2
2
] CH CH CH(~)CH OH
3
2
2
] CH CH(~)CH CH OH
2
2
3
2
2
nates,17h19 the unimolecular decomposition and isomerization
channels become important at elevated temperatures.4 For
sufficiently large alkoxyl radicals, isomerizations, in particular
1,5-isomerizations via six-member transition states, efficiently
compete with the decomposition steps and the H abstraction
] ~CH CH CH CH OH
2
2
2
2
] CH CH CH (~) ] HCHO
3
2
2
] H~ ] CH CH CH CHO
(7)
3
2
2
by O .17h20 The simplest radical exhibiting this feature is 1-
2
butoxyl, 1-C H O. Therefore, it can serve as a prototype for
The 1-C H O radicals formed in reaction (1b) are highly
4
9
4
9
the kinetic behaviour of the higher alkoxyl radicals.
Alkoxyl radicals can be generated by the reaction of alkyl
radicals with oxygen atoms. Accordingly, in the course of the
reaction
excited, with an average energy of D400 kJ mol~1. Conse-
quently, their kinetics has to be described in terms of the spe-
ciÐc rate coefficients k (E) for the reactions (i \ 2È7). A
i
comparison with results from thermal experiments, if avail-
able, and quantum chemical calculations can be accomplished
by unimolecular rate theory.21h23
1-C H ] O ] products
(1)
4
9
In the present study, we report on the experimental deter-
mination of the relative product yields for reaction (1). A
model capable of describing the basic Ðndings in a quantitat-
ive way was developed. The results of quantum chemical cal-
culations at di†erent levels are related to the experimental
observables by statistical rate theory. In this way, the branch-
ing ratios for reactions (1a) and (1b) as well as for reactions
(2)È(7) can be determined, and reasonable threshold energies
for the unimolecular reactions of 1-C H O are obtained.
1-butoxyl radicals are formed intermediately, probably in
competition to H abstraction:
1-C H ] O ] 1-C H ] OH
(1a)
(1b)
4
9
4 8
1-C H ] O ] 1-C H O
4
9
4 9
Therefore, the Ðnal product branching of reaction (1) to a
large part reÑects the competition between the unimolecular
4
9
DOI: 10.1039/b100149n
Phys. Chem. Chem. Phys., 2001, 3, 2365È2371
This journal is ( The Owner Societies 2001
2365

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a UV-spectrometer (Cary 5 UV-VIS-NIR Spectrophotometer,
2. Experimental
Varian) [e(1-C H I) \ 53.2 m2 mol~1; e(SO ) \ 240 m2
4
9
2
mol~1, see also ref. 25; j \ 190È195 nm; p \ 1È6 mbar;
T \ 295 K]. The IR absorption coefficients of the reactants
and the products were determined by the standard procedures
(absorbance vs. concentration) for authentic samples in the
wavelength region of minimal spectral interferences (see
below).
2.1. Experimental arrangements
Two di†erent arrangements were used in order to identify and
quantify the primary products of the O ] 1-C H reaction,
experimentally realized by the simultaneous photolysis of
4
9
the precursors SO (SO ] O ] SO) and 1-C H I (1-
2
2
4 9
C H I ] 1-C H ] I) combined with di†erent spectroscopic
The chemicals were of commercial grade [He (P99.995%),
4
9
4 9
methods and time resolution.
SO (P99.98%), Messer Griesheim; 1-C H I ([99%), 1-
2
4 9
C H ([99%) Merck; 1-C H CHO (P99%), Fluka].
4
8
3 7
2.1.1. UV-laser photolysis cell with laser induced Ñuores-
cence (LIF). The experimental set-up is shown schematically
in Fig. 1. The Ñowing mixture of SO ÈC H I highly diluted by
2.2. Experimental results
2
4 9
He was photolyzed in a quasi-static reaction vessel by an
excimer laser at 193 nm, allowing the total exchange of the
reaction mixture between two photolytic laser pulses. The OH
radicals in the vibrational state v \ 0, 1, 2 were detected by
the pump/probe technique via the A 2&` ^ X 2% transition in
the wavelength region of 306.4È318.5 nm by saturating the
transitions to the electronically excited states and measuring
the Ñuorescence. (Saturation reduces the dependence of the
LIF signal on the Ñuctuations of the laser Ñuence.) By the
variable time delay between the photolysis laser pulse and the
probe laser a time resolution of 0È400 ls was achieved. For
details of the detection system see for example ref. 24.
2.2.1. Formation of OH radicals by reaction (1a) as
detected by LIF. In order to elucidate the mechanism of the
primary attack in the C H ] O reaction the population of
4
9
the di†erent vibrational states of the primarily formed OH
radical has been studied: a thermal distribution of OH would
point to a complex formation of C H O with statistically con-
4
9
trolled decomposition C H O ] C H ] OH; a highly non-
4
9
4 8
thermal distribution would point to a direct route via
abstraction along O ] C H ] C H ] OH. Time-resolved
4
9
4 8
measurements were performed in order to estimate the contri-
bution of collisional relaxation to the measured population.
The formation of OH radicals in the ground and the Ðrst
and second excited vibrational states (v \ 0, 1, 2) was mea-
sured as a function of the reaction time for highly diluted mix-
tures, as displayed in Fig. 2. The measured signal intensities
were converted to relative concentrations via the known Ein-
stein coefficients found in the literature.26,27 In the absence of
one reaction partner, SO or C H I, respectively, no OH for-
2.1.2. UV-laser photolysis cell with FTIR spectrometer. In
a vacuum-tight stainless steel sphere (volume: 4 l) the mixture
of SO ] C H I partly diluted by Ar was photolyzed by an
2
4 9
excimer laser at 193 nm (Lambda Physik EMG 102). Typical
operation conditions were: laser beam proÐle of 6 mm ] 20
mm, laser energy of 10È60 mJ, repetition rate of 0.5È3 Hz.
Perpendicular to the laser beam a multiple pass mirror system
of the White type (40 traversals, 8 m optical path) was coupled
to an FTIR spectrometer for the optical absorption measure-
ments [Bruker IFS 66; MCT (Hg/Cd/Te) detector]. For
species identiÐcation and quantiÐcation, the spectral region
(600È5000 cm~1) and spectral resolution (0.11È4 cm~1) were
selected according to the lowest spectral interference and the
accuracy by the number of scans (20È500). To give some
examples: the simultaneous detection of the main products
HCHO/C H CHO was achieved around 1745 cm~1, the
2
4 9
mation was detected. As can be deduced from Fig. 2, the
excited states v \ 1, 2 are highly populated with a non-
thermal distribution (see the Discussion) with a maximum at a
reaction time of around 50 ls. The ground state (v \ 0)
exhibits the maximum at around 100 ls. This later maximum
is explained by the relaxation of the excited states after 50 ls
to the ground state, which is also semi-quantitatively reÑected
by the reduction of OH(v \ 1, 2) between 50 and 100 ls and
the increase of OH(v \ 0). The relaxation times for the pro-
cesses OH(v \ 1) ] He ] OH(v \ 0) ] He and OH(v \ 1)
] SO ] OH(v \ 0) ] SO have been reported recently by
3
7
search for the absent product C H in the presence of the
2
2
2
4
Hippler et al.28
main product 1-C H around 950 cm~1, both with a spectral
4
8
resolution of 1 cm~1. The detection sensitivity of C H
2
4
(signal-to-noise ratio of 3, 500 scans) was 5 ] 10~5 mbar
(2 ] 10~12 mol cm~3). The reaction vessel was equipped with
a gas handling system, pressure transducers, heaters, and a
pumping device. Details will be published elsewhere.
In order to estimate the concentrations of the 1-C H rad-
4
9
icals and the O atoms formed by photolysis at 193 nm the
absorption coefficients of 1-C H I and SO were measured by
4
9
2
Fig. 2 The reaction 1-C H ] O: Formation of the OH radical in
4
9
the vibrational states v \ 0, 1, 2 as observed by LIF (p \ 21.4 mbar;
T \ 294 K; [1-C H I] \ 2.2 ] 10~10 mol cm~3; [SO ] \ 7.0
4
9
0
2 0
] 10~10 mol cm~3; estimated concentrations: [1-C H ] \ 5.2
4
9 0
Fig. 1 Experimental arrangement.
] 10~12 mol cm~3, [O] \ 7.2 ] 10~11 mol cm~3).
0
2366
Phys. Chem. Chem. Phys., 2001, 3, 2365È2371

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For the simulation of the inÑuence of secondary reactions
on the primary product formation, a rate coefficient for reac-
tion (1) was needed. An approximate value was estimated
from three di†erent experimental approaches in our labor-
atory: (1) from the time-resolved proÐles of OH(v \ 0, 1, 2),
(2) from the competition between the reaction O ] C H
4
9
8
and the reference reaction 1-C H ] 1-C H ] 1-C H
4
9
4
9
4
] C H /hydrocarbons29 via the variation of the
4
0
10
4
[O] /[C H ] ratio and (3) from the fast Ñow reactor studies
9 0
of the reaction O ] 2-C H and the mixed reaction O
4
9
] (1C H ] 2-C H ). All three values were centered in the
4
9
4 9
range of (2È3) ] 1014 cm3 mol~1 s~1 with a weighted average
value of (2.4 ^ 0.6) ] 1014 cm3 mol~1 s~1. A more quantitat-
ive direct determination of k is under way.
1
The population inversion of the vibrational states of OH in
other alkyl radical ] oxygen atom reactions has been
observed by Leone et al.30 using the infrared chemilumine-
scence of OH (X 2%, v \ 1È5) at low pressure. As the v \ 0
state is not accessible by this method, the population of the
v \ 0 state was deduced by a surprisal analysis. The experi-
ments gave a nonÈthermal distribution of OH(v \ 0È5) for the
reactions O ] C H , O ] 1-C H and O ] 2-C H .
Fig. 4 The reaction 1-C H ] O: Formation of the stable reaction
4
9
products as a function of the photolyzed radical precursor 1-C H I
4
9
(p \ 1.0
mbar;
T \ 293
K;
[1-C H I] /[SO ] \ 3/4;
2 0
4
9 0
[1-C H ] /[O] \ 1/5.8).
4
9 0
0
primary and the various secondary reactions were performed.
These substantiated the assignment of the main primary
product channels with the following uncertainties: 1-C H
2
5
3
7
3 7
4
8
2.2.2. Formation of Ðnal products of reaction (1) as
detected by FTIR. In Fig. 3 the di†erence FTIR absorption
spectra are given for the reaction system at small and high
conversions with the assignment of the reaction products indi-
cating the spectral regions for a quantitative concentration
measurement via the absorbance. A search has been carried
out for the possible products C H , C H and C H OH, with
(0.55 ^ 0.08), HCHO (0.397 ^ 0.05), C H CHO (0.053 ^ 0.02).
3
7
The overall reaction scheme comprises the reactions of the
labile species O, OH, H, C H , C H , the precursors SO ,
1-C H I, and the products 1-C H , HCHO, C H CHO,
3
7
4
9
2
4
9
4
8
3 7
where the rate coefficients were taken from recent reviews or
estimated.31,32
2
4
3
6
3 5
a negative result. In Fig. 4 the relative calibrated concentra-
tions of the main products 1-C H , HCHO and C H CHO
3. Modeling of the product branching
4
8
3 7
are shown as a function of the depletion of the radical precur-
sor 1-C H I consumed by photolysis. Spectra were taken after
3.1. Quantum chemical calculations
4
9
every group of 500 laser pulses where the decrease of product
formation at the end of an experiment was due to a decrease
in laser pulse energy. In order to estimate the inÑuence of the
secondary photolysis of the aldehydic products on the
primary product yield, samples of the aldehydes of compara-
ble concentrations were photolyzed separately, leading to neg-
ligible changes in the branching ratios. The C H radical is a
co-product of reaction (6), and therefore the reaction C H
] O needs to be considered. As we have studied the reaction
of oxygen atoms with the homologous alkyl radicals CH ,
For the modeling of the branching ratios by statistical
unimolecular rate theory, the vibrational frequencies and rota-
tional constants of the 1-butoxyl radical and the transition
states for reactions (2)È(7) are required as well as the corre-
sponding threshold energies. The geometric data and fre-
quencies have been obtained by ab initio calculations at
MP2/6-31G* level, and the results are shown in Table 1. The
energetic parameters stem in part from ref. 4 and in part from
quantum chemical calculations carried out in the present
work. All ab initio calculations were performed using the
GAUSSIAN 94 program package.33
3
7
3
7
3
C H and C H for product formation like 1-C H the con-
2
5
3
7
4 9
tribution of the additional HCHO formation via O ] C H
3
7
could be estimated (O ] C H ] OH ] C H /HCHO
In recent studies,4,7,9h13 the capability of di†erent theoreti-
cal methods was tested to predict reliable energetic parameters
for b-bond dissociation reactions of alkoxyl radicals. A modi-
Ðed G2(MP2) approach7,9,10 is employed in the present work
to characterize the b-decomposition reactions and the 1,5-
isomerization step, which are the dominating unimolecular
reaction channels of 1-C H O.3,4 The original G2(MP2)
3
7
3 6
] C H /C H CHO ] H). In order to quantify the uncer-
2
5
2 5
tainties of the branching ratios, modeling studies of the
4
9
procedure34,35 is modiÐed insofar as the equilibrium geome-
tries, transition structures and harmonic frequencies are calcu-
lated at the MP2(fc)/6-31G* level, an alteration that is
discussed in more detail in refs. 7 and 9. The threshold ener-
gies at 0 K follow from the classical barrier heights [obtained
as the energy di†erences from the G2(MP2) model] by adding
the di†erences of the vibrational zero-point energies scaled by
a factor of 0.9646 as recommended by Pople et al.36 The
results are included in Table 2.
The threshold energy of the 1,5 H atom transfer obtained
by our G2(MP2)-like procedure agrees with results from dif-
ferent DFT methods3,4,11 and a BAC-MP4 calculation4
within 6 kJ mol~1. Also the agreement with a thermal activa-
Fig. 3 The reaction 1-C H ] O: Di†erence FTIR absorption spec-
4
9
tion energy of 41 kJ mol~1 determined by
a relative
trum of the products formed (]) and educts consumed ([). Indicated
spectral regions used for the quantitative concentration determination
via the absorbance.
measurement1 is reasonable, and, consequently, a value of
40 ^ 5 kJ mol~1 can be recommended for this threshold
Phys. Chem. Chem. Phys., 2001, 3, 2365È2371
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Table 1 Harmonic wavenumbers v (scaled by 0.9427)36 and rotational constants A, B and C as obtained from the ab initio calculations (MP2/6-
i
31G*)
v /cm~1
A, B, C/cm~1
i
1-C H O
106, 114, 179, 246, 374, 406, 489, 719, 824, 889, 972, 978, 1036, 1050, 1102,
1200, 1233, 1264, 1288, 1332, 1371, 1389, 1395, 1463, 1470, 1475, 1483,
2848, 2898, 2911, 2926, 2928, 2953, 2983, 3010, 3012
0.6638, 0.06742, 0.06412
4
9
TS(2)
2126i, 87, 105, 185, 244, 376, 433, 617, 724, 842, 887, 923, 995, 1046, 1092,
1114, 1136, 1218, 1244, 1284, 1332, 1368, 1389, 1454, 1468, 1475, 1482,
2458, 2895, 2920, 2927, 2956, 2961, 2975, 3010, 3013
0.6952, 0.06636, 0.06360
0.4151, 0.08542, 0.07940
0.3299, 0.1097, 0.09197
0.2357, 0.1589, 0.1071
0.6171, 0.06157, 0.05852
0.4963, 0.07725, 0.07332
TS(3)
TS(4)
TS(5)
TS(6)
TS(7)
2215i, 97, 147, 238, 261, 416, 672, 708, 807, 856, 926, 957, 1018, 1076, 1102,
1107, 1131, 1157, 1240, 1254, 1279, 1363, 1389, 1455, 1473, 1477, 1498,
1954, 2905, 2928, 2934, 2960, 2993, 3012, 3016, 3016
2408i, 141, 205, 229, 355, 514, 594, 740, 822, 889, 929, 956, 991, 1060, 1103,
1135, 1174, 1205, 1240, 1262, 1321, 1343, 1383, 1457, 1462, 1466, 1490,
1773, 2888, 2913, 2935, 2959, 2975, 2992, 2995, 3022
2141i, 162, 306, 383, 436, 482, 645, 803, 831, 874, 919, 934, 1009, 1049,
1098, 1137, 1157, 1206, 1230, 1255, 1306, 1329, 1340, 1429, 1452, 1459,
1470, 1529, 2866, 2917, 2924, 2935, 2968, 2979, 2989, 3060
551i, 67, 86, 147, 245, 320, 365, 579, 707, 745, 870, 888, 890, 1011, 1083,
1147, 1188, 1223, 1280, 1310, 1380, 1448, 1465, 1472, 1477, 1484, 1644,
2789, 2846, 2931, 2933, 2982, 3018, 3024, 3028, 3125
1630i, 97, 105, 222, 248, 341, 510, 560, 617, 731, 851, 876, 950, 1026, 1034,
1114, 1147, 1226, 1260, 1289, 1344, 1363, 1388, 1449, 1468, 1474, 1480,
1630, 2780, 2923, 2927, 2934, 2978, 3003, 3013, 3015
energy. For the b-CÈC bond dissociation, the modiÐed
G2(MP2) barrier height agrees with results from
DFT4,10,11,13(a) and BAC-MP44,11 computations within ^8
kJ mol~1. The barrier obtained from corrected MP4 calcu-
lations,4 however, is lower by ca. 10 kJ mol~1 and those from
CBS calculations3,13(a) are lower by ca. 10È20 kJ mol~1. For
the b-CÈH bond dissociation, the barrier heights at
BAC-MP4 and B3LYP/6-311]G(2d,p) level4 exceed those
from our G2(MP2) calculations by D12 kJ mol~1 and D3 kJ
mol~1, respectively.
3.2. Statistical unimolecular rate theory
The branching ratios between the di†erent unimolecular reac-
tion channels of 1-C H O under our experimental conditions
4
9
can be expressed in terms of the respective low-pressure limit-
ing rate coefficients for chemical activation:21h23
r
r
k
k
m
0m
0n
\
(8)
(9)
n
Here, r is the rate of reaction for channel j and
j
For reactions (5), (6) and (7), the agreement between the
activation parameters from DFT-B3LYP3,4 and from the
more expensive G2(MP2) and BAC-MP44 calculations is rea-
sonable. Therefore, a geometry optimization at MP2/6-31G*
level (or higher) combined with a DFT-B3LYP37,38 or a
G2(MP2) energy calculation should allow for a reasonable
description of the unimolecular reactions of alkoxyl radicals.
We note that for the two b-bond dissociation reactions (6) and
(7), the most product-like transition structures were obtained
by the DFT calculations and the least product-like at the
MP2/6-31G* level.3,4 This is discussed in detail in ref. 9 for
the case of C H O.
P=
k
\
k (E)Fss(E) dE
j
0j
E0,min
with the normalized steady-state distribution for 1-C H O
4
9
3 4
~1
F(E)
P
=
F(E) dE
; k (E)
i
Fss(E) \
(10)
; k (E)
i
E0,min
i
i
and the speciÐc rate coefficients k (E). Here E
denotes the
i
0, min
lowest threshold energy among the di†erent unimolecular
channels i. The nascent distribution of the 1-butoxyl radicals,
F(E), is approximated by21
2
5
In Section 4, the adequacy of the threshold energies will be
veriÐed by a comparison of the predicted branching ratios
with our experimental results.
W
(E [ Ear) exp[[(E [ Ear)/k T ]
1vC4H9O
0
0
B
F(E) \
(11)
P
=
W
(e) exp([e/k T ) de
1vC4H90
B
0
Table 2 Threshold energies at T \ 0 K as obtained from quantum
chemical calculations and the resulting high-pressure limiting Arrhe-
nius parameters for T \ 300 K based on the data from Table 1 and
the reaction path degeneracies given in the text
where k is BoltzmannÏs constant, T the temperature, W
B
1vC4H9O
the sum of states for 1-C H O and Ear the threshold energy
4
9
0
for the reaction 1-C H O ] 1-C H ] O. The speciÐc rate
4
9
4 9
coefficients follow from RRKM theory as21h23,39
Reaction E /kJ mol~1 Method
0i
lg(A /s~1) E /kJ mol~1
=
=
L W (E [ E )
(2)
(3)
(4)
(5)
(6)
(7)
105.0a
103.6a
70.79a
43.76
60.96
83.22
MP-SAC2 13.55
MP-SAC2 13.05
MP-SAC2 12.57
107.3
104.7
70.91
42.68
64.16
85.64
i
i
0i
k (E) \
(12)
i
ho
(E)
1vC4H9O
where h is PlanckÏs constant, o
the density of states of
1-C H O, E the threshold energy for channel i and W the
G2(MP2)
G2(MP2)
G2(MP2)
12.06
13.76
13.52
1vC4H9O
4
9
0i
i
sum of states of the corresponding transition state. Symmetry
e†ects are explicitly expressed in terms of reaction path degen-
a Ref. 4.
eracies L . The energy E is counted from the vibrational
i
2368
Phys. Chem. Chem. Phys., 2001, 3, 2365È2371

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exact treatment, the full hindered rotor phase space of the 1-
butoxyl radical would have to be sampled in calculating the
density of states. Because these hindered rotations disappear
in the cyclic transition states, a formal value of L \ 2 would
i
result.22 We used this value as an approximation in the case
of reactions (3)È(5), even though we calculated the density of
states for harmonic torsional vibrations. We note that the
branching between reactions (2), (6) and (7) is not inÑuenced
by this choice.
4. Discussion
The speciÐc rate coefficients computed with the parameters
from Tables 1 and 2 are shown in Fig. 6. The resulting low-
pressure limiting rate coefficients for the unimolecular chan-
nels and the relative branching fractions are contained in
Table 3. Among the reactions of 1-C H O, the b-CÈC bond
dissociation dominates with a fractional contribution of
D70% followed by the b-CÈH bond split with D18%. The
isomerization steps on the whole contribute with D12%,
where nearly one half can be assigned to the 1,5 H shift.
Though the latter reaction has the lowest threshold energy, its
speciÐc rate coefficients fall below those of the decomposition
channels at high excitation energies because of the tightness of
the cyclic transition state (cf. Fig. 6).
Fig. 5 Schematic energy diagram for the formation and subsequent
unimolecular reaction of 1-C H O.
4
9
4
9
ground state of 1-C H O, and some of the relevant quantities
4
9
are illustrated in Fig. 5. The thermochemical limit Ear is
0
approximated by the di†erence of the heats of formation at
298 K for 1-C H ] O and 1-C H O. The following values
4
9
4 9
(in kJ mol~1) have been used: 1-C H , 80.9;40 O, 249.2;41
4
9
and 1-C H O, 62.8;41 it follows that Ear \ 392.9 kJ mol~1. By
4
9
0
adding the mean energy of the distribution function F(E), an
average excitation energy of 407.0 kJ mol~1 is obtained for
the nascent 1-C H O population.
In characterizing the product yields, it is important to con-
sider the fate of the carbon-centered radicals that follow from
the isomerization steps (2)È(5). Apart from subsequent isomer-
izations, including the reverse reactions to 1-C H O, the most
4
9
The sums and densities of states were exactly counted,42
using the molecular parameters from Section 3.1. The conser-
vation of total angular momentum was taken into account.43
From the thermal rotational distribution of 1-C H at 300 K
4
9
important consecutive steps of these species are the b-CÈC
bond dissociation reactions, which would lead to the following
stable products: H CCHOH for reaction (2), H CCHCH OH
4
9
2
2
2
and the orbital angular momentum caused by the capture
process, 1-C H ] O, an average rotational excitation of
4
9
SJT B 60 follows for the nascent 1-C H O population.44,45
4
9
Accordingly, all sums and densities of states were calculated
for J \ 60. It should be noted, however, that due to the tight
transition states in this system, the branching ratios are vir-
tually independent of the rotational excitation.
For the reaction path degeneracy L , we used a value of 1
i
for reaction (6) and 2 for all other reactions; however, some
remarks regarding these numbers are necessary. The general
approach to determining reaction path degeneracies was
reviewed in ref. 46, and a thorough representation of this topic
can also be found in ref. 22. The situation is quite clear in the
case of reactions (2), (6) and (7). By considering all permu-
tations between like atoms in the 1-butoxyl radical and the
corresponding transition state and by correlating the mutually
accessible conÐgurations, the above values are obtained in a
straightforward manner. It is unimportant whether the trans
or the gauche conformation of the 1-butoxyl radical is con-
sidered as the reactant equilibrium structure or whether the
torsions are treated as hindered rotations. For these reactions,
the 1-C H group simply acts as a spectator. The situation
Fig. 6 Nascent distribution of 1-C H O and speciÐc rate coefficients
4
9
for reactions (2)È(7); threshold energies from Table 2. For the disso-
ciation reactions, the breaking bond is given.
3
7
becomes more complex for reactions (3)È(5). Because the
overall symmetry numbers for the 1-butoxyl radical as well as
for the transition states are unity, the reaction path degener-
acy is the ratio of the respective numbers of optical isomers:22
Table 3 Low-pressure limiting rate coefficients and relative branch-
ing fractions Y
i
Reaction
k /s~1
0i
Y a
Y b
Y c
Exp.
0.55
i
i
i
(1a)
(2)
(3)
(4)
(5)
(6)
(7)
0.0
0.55
0.55
m
i
L \
9.9 ] 1010
3.5 ] 1010
1.0 ] 1011
1.9 ] 1011
2.3 ] 1012
6.0 ] 1011
0.030
0.011
0.030
0.057
0.692
0.180
0.014
0.005
0.014
0.026
0.310
0.081
0.011
0.004
0.011
0.021
0.354
0.049
i
m
1vC4H9O
The transition states 3È5 are asymmetric, and hence m \ 2.
i
For the 1-butoxyl radical, however, m
\ 1 in the trans
0.397
0.053
1vC4H9O
and m
\ 2 in the gauche conformation. Accordingly,
1vC4H9O
the reaction path degeneracies are 2 and 1, respectively.
Because both conformations di†er in energy by only D3 kJ
mol~1 (ref. 47), they are comparably populated even at room
temperature. At this point, the approximate character of the
concept of reaction path degeneracy becomes obvious. In an
a Reaction (1a) neglected. b Relative branching fraction of reaction
(1a) set equal to the experimental 1-C H yield (see text).
4
8
c Recommended values E \ 55 kJ mol~1 and E \ 88 kJ mol~1
06 07
used.
Phys. Chem. Chem. Phys., 2001, 3, 2365È2371
2369

View Article Online
for reaction (3), C H for reaction (4) and C H for reaction
ref. 50. We obtained relative populations of 1, 5.5 ] 10~2,
3
6
2 4
(5). None of these products, however, was observed in our
experiments. Obviously, the back isomerizations and/or other
reactions dominate.
2.5 ] 10~3 and 9.2 ] 10~5 for the vibrational states v \ 0,
OH
1, 2 and 3, respectively, which is clearly di†erent from the dis-
tribution observed. This indicates that reaction (1a) probably
Stable species that we did observe, and that can be attrib-
uted at least in part to the isomerization channels, are 1-
C H CHO and 1-C H . Butyraldehyde, which is the product
is a direct abstraction process.51
3
7
4 8
5. Conclusions
of reaction (7), can also be formed as a result of reaction (2) by
a b-OÈH bond split of the a-hydroxy-1-butyl radical. The
energetically favourable decomposition path of this radical,
however, is the b-CÈC bond dissociation as mentioned above.
Accordingly, the OÈH bond split plays only a minor role, and
the fractional contribution of this reaction route to the pro-
duction of 1-C H CHO should be negligible and by far below
The 1-C H ] O reaction is likely to proceed via two parallel
4
9
channels, which contribute nearly equally to the overall reac-
tion. One is probably a direct abstraction channel leading to
1-C H and OH, and the second is an association process
4
8
resulting in a chemically activated 1-butoxyl radical. Under
low-pressure conditions, the latter essentially undergoes
b-CÈC and b-CÈH bond dissociation. Isomerization products
are not observed. The branching between these channels can
be described by statistical rate theory using results from
quantum chemical calculations. In this way, reliable threshold
energies can be obtained.
3
7
its hypothetical maximum value of Y /(Y ] Y ) B 0.14 (cf.
2
2
7
Table 3). Therefore, the observed butyraldehyde yield is solely
attributed to reaction (7).
1-Butene can result from an OH split-o† from
CH CH CHÉCH OH, which is the product of reaction (3).
3
2
2
However, there is again an energetically favoured parallel
channel leading to H CCHCH OH ] CH . Anyway, reaction
2
2
3
Acknowledgements
(3) alone would result in a 1-butene yield of at most D1%, as
becomes obvious from Table 3, and hence the observed yield
of 55% cannot be explained by unimolecular isomerization/
decomposition steps of the intermediate C H O radical.
Funding by the Deutsche Forschungsgemeinschaft (SFB 357
““Molekulare Mechanismen Unimolekularer ProzesseÏÏ) and
the Fonds der Chemischen Industrie is gratefully acknow-
ledged. M.O. would like to thank Prof. K. Scherzer for contin-
uous support. B.V. is grateful for a Magyary Zoltan (AMFK
535/2) and Eotvos postdoctoral fellowship as well as for Ðnan-
cial support by the Hungarian ScientiÐc Research Fund
(OTKA F030436). The ab initio calculations were carried out
at the Regionales Rechenzentrum fur Niedersachsen Hanno-
ver.
4
9
Apparently, there is a direct route leading from 1-C H ] O
4
9
to 1-C H ] OH [reaction (1a)] with a fractional contribu-
tion of D55% to the overall reaction. The nature of this route
is not quite clear; however, some evidence for a direct meta-
thesis will be given below.
4
8
The third stable product detected, HCHO, can be unam-
biguously attributed to the b-CÈC bond dissociation of 1-
C H O, reaction (6). Consequently, with the premises just
4
9
stated, the observed ratio [HCHO]/[1-C H CHO] reÑects
3
7
the branching between reactions (6) and (7), a correspondence
that can be used to verify in part the results of our quantum
chemical calculations.
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7
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06
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2371